Details

Time bar (total: 39.4s)

sample64.0ms

Algorithm
intervals
Results
16.0ms185×body80valid
11.0ms29×body1280valid
10.0ms256×pre80true
9.0ms24×body640valid
4.0ms15×body320valid
0.0ms3×body160valid

simplify143.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
143.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize15.0ms

Local error

Found 2 expressions with local error:

1.4b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
26×add-sqr-sqrt
25×times-frac
19×distribute-lft-out
14×add-cube-cbrt
6×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-cbrt-cube add-exp-log add-log-exp
2×pow1 flip3-+ div-sub associate-/r/ flip-+ insert-posit16 associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg flip3-- div-exp associate-+l- div-inv flip--
Counts
2 → 67
Calls
2 calls:
Slowest
118.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
59.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series152.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
82.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
70.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify3.4s

Counts
74 → 73
Calls
74 calls:
Slowest
280.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
241.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
185.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
183.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
170.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))

prune739.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.0b

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
61×add-sqr-sqrt
56×times-frac
36×add-cube-cbrt
24×distribute-lft-out
13×associate-/r* associate-/l* distribute-lft-out--
10×add-cbrt-cube add-exp-log difference-of-squares
6×add-log-exp
4×pow1 associate-/r/ insert-posit16 associate-/l/
3×cbrt-undiv clear-num frac-2neg flip3-- div-exp div-inv flip--
2×flip3-+ frac-sub flip-+
1×sub-neg diff-log div-sub
Counts
4 → 141
Calls
4 calls:
Slowest
870.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
119.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
43.0ms
(/ alpha (+ (+ alpha beta) 2.0))
43.0ms
(/ beta (+ (+ alpha beta) 2.0))

series341.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
101.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
98.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
85.0ms
(/ beta (+ (+ alpha beta) 2.0))
57.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify10.2s

Counts
155 → 153
Calls
155 calls:
Slowest
510.0ms
(/ (* (cbrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (cbrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (cbrt 2.0) (cbrt 2.0)))
438.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
412.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
369.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
269.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.4b

localize35.0ms

Local error

Found 4 expressions with local error:

6.3b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.3b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.3b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
1.4b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
63×cbrt-prod
46×times-frac
36×add-sqr-sqrt
31×add-cube-cbrt
27×distribute-lft-out
6×associate-/r/ add-log-exp
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×cbrt-div flip3-+ pow1/3 flip-+ div-inv
2×difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 109
Calls
4 calls:
Slowest
145.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
24.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
10.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
10.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series715.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
226.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
197.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
196.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
97.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify4.8s

Counts
84 → 121
Calls
84 calls:
Slowest
268.0ms
(- (exp (* 1/3 (+ (log beta) (log 0.5)))) (+ (* 0.16666666666666666 (* beta (exp (* 1/3 (+ (log beta) (log 0.5)))))) (* 0.16666666666666666 (* (exp (* 1/3 (+ (log beta) (log 0.5)))) alpha))))
247.0ms
(- (exp (* 1/3 (+ (log beta) (log 0.5)))) (+ (* 0.16666666666666666 (* beta (exp (* 1/3 (+ (log beta) (log 0.5)))))) (* 0.16666666666666666 (* (exp (* 1/3 (+ (log beta) (log 0.5)))) alpha))))
239.0ms
(- (exp (* 1/3 (+ (log beta) (log 0.5)))) (+ (* 0.16666666666666666 (* beta (exp (* 1/3 (+ (log beta) (log 0.5)))))) (* 0.16666666666666666 (* (exp (* 1/3 (+ (log beta) (log 0.5)))) alpha))))
215.0ms
(cbrt (/ beta (+ (pow (+ alpha beta) 3) (pow 2.0 3))))
209.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.4b

localize47.0ms

Local error

Found 4 expressions with local error:

8.1b
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
1.4b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.8b
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
0.0b
(/ beta (+ (+ alpha beta) 2.0))

rewrite751.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
72×add-sqr-sqrt
64×times-frac
50×log-prod
37×add-cube-cbrt
25×exp-sum
19×distribute-lft-out--
14×difference-of-squares
12×distribute-lft-out
9×add-exp-log
6×pow1 add-cbrt-cube add-log-exp
5×associate-/r*
4×exp-prod insert-posit16
3×div-inv associate-/l*
2×log-div div-exp rem-log-exp associate-/r/ log-pow
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ flip3-- exp-diff diff-log flip-+ flip-- rem-exp-log
Counts
4 → 130
Calls
4 calls:
Slowest
273.0ms
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
258.0ms
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
173.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
43.0ms
(/ beta (+ (+ alpha beta) 2.0))

series474.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
215.0ms
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
105.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
87.0ms
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
67.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify8.7s

Counts
118 → 142
Calls
118 calls:
Slowest
293.0ms
(exp (* (cbrt (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))) (cbrt (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))))
287.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
283.0ms
(exp (log (/ (* (cbrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (cbrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (cbrt 2.0) (cbrt 2.0)))))
269.0ms
(log (/ (* (cbrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (cbrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (cbrt 2.0) (cbrt 2.0))))
228.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.3b

regimes210.0ms

Accuracy

73.9% (3.2b remaining)

Error of 6.3b against oracle of 3.0b and baseline of 15.5b

bsearch83.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
800.0ms785×body1280valid
679.0ms5875×body80valid
389.0ms8000×pre80true
297.0ms730×body640valid
122.0ms400×body320valid
39.0ms210×body160valid